> WSiler wrote:> > > > >While I agree that we should not rule out a relationship between fuzzy> > >sets and probability ( indeed I am a strong advocate of probabilistic> > >semantics for fuzzy sets) I do not agree that we should take probability> > >distributions of random variables (normalised or not) as membership> > >functions of fuzzy sets. The former quantify uncertainty regarding the> > >value of a random variable and the other vagueness of definition.> > >> > It is certainly true that "probability distributions quantify uncertainty> > regarding the value of a random variable", to say that "[membership functions> > of fuzzy sets characterize] vagueness of definition" is a quite unnecessary> > restriction on fuzzy sets. Having worked on real-world applications of fuzzy> > expert systems for some fifteen years now, I consider that fuzzy sets can> > characterize uncertainty of whatever origin, including both vagueness and> > values of random variables among many others.> > > > To assert that a normal distribution characterizes a numeric random variable> > subject to a large number of small errors amounts to a tautology, parameterized> > perhaps as a mean and variance. However, I can (and often do) characterize that> > same variable as a bell-shaped fuzzy number, paramaterized perhaps as central> > value and a hedge "roughly". There is no vagueness here, just an uncertainty as> > to precise value. In an expert system, "roughly 2" is a heck of a lot more> > useful than "2 +/- 25%".> > > > A list of the kinds of uncertainty which can be fruitfully represented by fuzzy> > quantities (e.g. truth values of scalars, fuzzy numbers, membership functions,> > truth values of rules, truth values of members of a discrete fuzzy set,...)> > would probably be quite long. If I'm not sure that a car is a Ford or a> > Chevrolet, that uncertainty is easily represented by the grades of membership> > in a discrete fuzzy set of car makes, for example.> > Bill:> > Thanks for the automobile lead-in...> > To help me understand some of the points raised, allow me to pose a> problem:> > I own a Mercury Villager mini-van, which is made in the same factory as> the Nissan Quest (in Ohio, by the way), and most of the parts are> identical and interchangeable. As you might assume, they look very> similar. Now, if I see 2 mini-vans in a parking lot, and they appear to> be a Villager/Quest, but I can't tell from the distance I am at, than> the probability that the one on the left is a Villager is .5, and the> probability that it is a Quest is .5 (the same goes for the one on the> right).> > Now, if I walk out into the parking lot and inspect the 2 vehicles, I> find that the one on the left is a Quest and the one on the right is> also a Quest. The probability now is 0.0 that either one is a> Villager. But what about the membership in the set (classification,> identity, whatever) of Villager? I would say that the Quest has a> membership of .95 in the set of Villager (and vice versa). How does> probability help explain to a mechanic that he can fix a Villager if he> has only ever fixed Quests before?> > Tony

In the problem you propose, you would need to use "similarity". The more
similarity there is between 2 elements, the less they exculde each other.

This is why a mechanic can fix a Villager the first time he sees one.
Because it is very similar to the Quest, which he is used to.

############################################################################
This message was posted through the fuzzy mailing list.
(1) To subscribe to this mailing list, send a message body of
"SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
(2) To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
to listproc@dbai.tuwien.ac.at
(3) To reach the human who maintains the list, send mail to
fuzzy-owner@dbai.tuwien.ac.at
(4) WWW access and other information on Fuzzy Sets and Logic seehttp://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html